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2014 Fiscal Year Annual Research Report

解空間の直径に基づく計算限界解析アプローチの構築

Publicly Offered Research

Project AreaA multifaceted approach toward understanding the limitations of computation
Project/Area Number 25106504
Research InstitutionTohoku University

Principal Investigator

伊藤 健洋  東北大学, 情報科学研究科, 准教授 (40431548)

Project Period (FY) 2013-04-01 – 2015-03-31
Keywordsアルゴリズム / グラフ / 独立点集合 / 点彩色
Outline of Annual Research Achievements

本年度は,点彩色を一般化した「リスト点彩色」の遷移問題に対して,詳細な解析を与えることができた.グラフ構造の指標として「パス幅」と呼ばれるパラメータがあるが,パス幅が2以上であればリスト点彩色の遷移問題はPSPACE完全であり,パス幅が1であれば多項式時間で解けることを示した.すなわち,これはリスト点彩色の遷移問題の計算困難性と容易性を,入力グラフのパス幅の観点から特徴づけたことになる.パス幅1の入力グラフに対する多項式時間アルゴリズムは動的計画法に基づいており,遷移問題に対して動的計画法を適用した例としても評価できる.

また,独立点集合の遷移問題に対しては,固定パラメータ容易性(FPT)の観点から,研究を進めることができた.この問題は,平面グラフにおいてPSPACE完全であることが示されており,解空間グラフの直径は超多項式長になる.しかし本研究では,独立点集合のサイズのみをパラメータとして,平面グラフに対するFPTアルゴリズムを与えた.この研究成果により,解空間グラフの直径が超多項式長になることを単に示すだけでなく,パラメータにどのように依存するのか解析することができた.特に,本研究では昨年度,一般のグラフに対しては,独立点集合のサイズのみをパラメータとしたFPTアルゴリズムを持ちそうにないことを証明しており,今年度の研究と対比させることで,入力グラフの構造と計算困難性の関係をより具体的に解析することができた.

この他にも,点彩色と関連が深いL(2,1)ラベリングなど,様々な遷移問題に対してアルゴリズムを開発することで,解空間グラフの直径が多項式長で抑えられる場合を明らかにし,計算困難である場合との対比を可能とした.特に,本研究では,入力グラフの構造を上手く利用することで,効率のよいアルゴリズムを多数開発することができた.

Research Progress Status

26年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

26年度が最終年度であるため、記入しない。

  • Research Products

    (23 results)

All 2015 2014

All Journal Article (15 results) (of which Peer Reviewed: 15 results,  Acknowledgement Compliant: 15 results,  Open Access: 1 results) Presentation (8 results)

  • [Journal Article] Swapping Labeled Tokens on Graphs2015

    • Author(s)
      Katsuhisa Yamanaka, Erik D. Demaine, Takehiro Ito, Jun Kawahara, Masashi Kiyomi, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Kei Uchizawa, Takeaki Uno
    • Journal Title

      Theoretical Computer Science

      Volume: 印刷中 Pages: 印刷中

    • DOI

      10.1016/j.tcs.2015.01.052

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs2015

    • Author(s)
      Tatsuhiko Hatanaka, Takehiro Ito, Xiao Zhou
    • Journal Title

      IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Algorithms for the Independent Feedback Vertex Set Problem2015

    • Author(s)
      Yuma Tamura, Takehiro Ito, Xiao Zhou
    • Journal Title

      IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Reconfiguration of Cliques in a Graph2015

    • Author(s)
      Takehiro Ito, Hirotaka Ono, Yota Otachi
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Reconfiguration of Vertex Covers in a Graph2015

    • Author(s)
      Takehiro Ito, Hiroyuki Nooka, Xiao Zhou
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Deterministic Algorithms for the Independent Feedback Vertex Set Problem2015

    • Author(s)
      Yuma Tamura, Takehiro Ito, Xiao Zhou
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 印刷中 Pages: 印刷中

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Experimental Evaluations of Dynamic Algorithm for Maintaining Shortest-Paths Trees on Real-World Networks2015

    • Author(s)
      Takashi Hasegawa, Takehiro Ito, Akira Suzuki, Xiao Zhou
    • Journal Title

      Interdisciplinary Information Sciences

      Volume: 21 Pages: 25-35

    • DOI

      10.4036/iis.2015.25

    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Complexity of Finding Maximum Regular Induced Subgraphs with Prescribed Degree2014

    • Author(s)
      Yuichi Asahiro, Hiroshi Eto, Takehiro Ito, Eiji Miyano
    • Journal Title

      Theoretical Computer Science

      Volume: 550 Pages: 21-35

    • DOI

      10.1016/j.tcs.2014.07.008

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A 4.31-Approximation for the Geometric Unique Coverage Problem on Unit Disks2014

    • Author(s)
      Takehiro Ito, Shin-ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, Yushi Uno
    • Journal Title

      Theoretical Computer Science

      Volume: 544 Pages: 14-31

    • DOI

      10.1016/j.tcs.2014.04.014

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Reconfiguration of List L(2,1)-Labelings in a Graph2014

    • Author(s)
      Takehiro Ito, Kazuto Kawamura, Hirotaka Ono, Xiao Zhou
    • Journal Title

      Theoretical Computer Science

      Volume: 544 Pages: 84-97

    • DOI

      10.1016/j.tcs.2014.04.011

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs2014

    • Author(s)
      Tatsuhiko Hatanaka, Takehiro Ito, Xiao Zhou
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8881 Pages: 314-328

    • DOI

      10.1007/978-3-319-12691-3_24

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The Minimum Vulnerability Problem on Graphs2014

    • Author(s)
      Yusuke Aoki, Bjarni V. Halldorsson, Magnus M. Halldorsson, Takehiro Ito, Christian Konrad, Xiao Zhou
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8881 Pages: 299-313

    • DOI

      10.1007/978-3-319-12691-3_23

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Polynomial-Time Algorithm for Sliding Tokens on Trees2014

    • Author(s)
      Erik D. Demaine, Martin L. Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, Takeshi Yamada
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8889 Pages: 389-400

    • DOI

      10.1007/978-3-319-13075-0_31

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Fixed-Parameter Tractability of Token Jumping on Planar Graphs2014

    • Author(s)
      Takehiro Ito, Marcin Kaminski, Hirotaka Ono
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8889 Pages: 208-219

    • DOI

      10.1007/978-3-319-13075-0_17

    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Minimum-Cost b-Edge Dominating Sets on Trees2014

    • Author(s)
      Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 8889 Pages: 195-207

    • DOI

      10.1007/978-3-319-13075-0_16

    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Reconfiguration of Cliques in a Graph2015

    • Author(s)
      Takehiro Ito, Hirotaka Ono, Yota Otachi
    • Organizer
      12th Annual Conference on Theory and Applications of Models of Computation
    • Place of Presentation
      シンガポール
    • Year and Date
      2015-05-19
  • [Presentation] The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs2014

    • Author(s)
      Tatsuhiko Hatanaka, Takehiro Ito, Xiao Zhou
    • Organizer
      8th Annual International Conference on Combinatorial Optimization and Applications
    • Place of Presentation
      ハワイ(アメリカ)
    • Year and Date
      2014-12-20
  • [Presentation] The Minimum Vulnerability Problem on Graphs2014

    • Author(s)
      Yusuke Aoki, Bjarni V. Halldorsson, Magnus M. Halldorsson, Takehiro Ito, Christian Konrad, Xiao Zhou
    • Organizer
      8th Annual International Conference on Combinatorial Optimization and Applications
    • Place of Presentation
      ハワイ(アメリカ)
    • Year and Date
      2014-12-20
  • [Presentation] Polynomial-Time Algorithm for Sliding Tokens on Trees2014

    • Author(s)
      Erik D. Demaine, Martin L. Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, Takeshi Yamada
    • Organizer
      25th Annual International Symposium on Algorithms and Computation
    • Place of Presentation
      全州(韓国)
    • Year and Date
      2014-12-16
  • [Presentation] Fixed-Parameter Tractability of Token Jumping on Planar Graphs2014

    • Author(s)
      Takehiro Ito, Marcin Kaminski, Hirotaka Ono
    • Organizer
      25th Annual International Symposium on Algorithms and Computation
    • Place of Presentation
      全州(韓国)
    • Year and Date
      2014-12-15
  • [Presentation] Minimum-Cost b-Edge Dominating Sets on Trees2014

    • Author(s)
      Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
    • Organizer
      25th Annual International Symposium on Algorithms and Computation
    • Place of Presentation
      全州(韓国)
    • Year and Date
      2014-12-15
  • [Presentation] Deterministic Algorithms for the Independent Feedback Vertex Set Problem2014

    • Author(s)
      Yuma Tamura, Takehiro Ito, Xiao Zhou
    • Organizer
      25th International Workshop on Combinatorial Algorithms
    • Place of Presentation
      ダルース(アメリカ)
    • Year and Date
      2014-10-17
  • [Presentation] Reconfiguration of Vertex Covers in a Graph2014

    • Author(s)
      Takehiro Ito, Hiroyuki Nooka, Xiao Zhou
    • Organizer
      25th International Workshop on Combinatorial Algorithms
    • Place of Presentation
      ダルース(アメリカ)
    • Year and Date
      2014-10-15

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Published: 2016-06-01  

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